Simplify; express your answer in exponential form. Assume $q\neq 0, a\neq 0$. $\dfrac{{(q^{-2})^{4}}}{{(q^{5}a^{-3})^{-3}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{-2}}$ to the exponent ${4}$ . Now ${-2 \times 4 = -8}$ , so ${(q^{-2})^{4} = q^{-8}}$ In the denominator, we can use the distributive property of exponents. ${(q^{5}a^{-3})^{-3} = (q^{5})^{-3}(a^{-3})^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q^{-2})^{4}}}{{(q^{5}a^{-3})^{-3}}} = \dfrac{{q^{-8}}}{{q^{-15}a^{9}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-8}}}{{q^{-15}a^{9}}} = \dfrac{{q^{-8}}}{{q^{-15}}} \cdot \dfrac{{1}}{{a^{9}}} = q^{{-8} - {(-15)}} \cdot a^{- {9}} = q^{7}a^{-9}$.